What is (\partial)/(\partial x)(e^{xy}y^2+x/y) ?

The answer to (\partial)/(\partial x)(e^{xy}y^2+x/y) is y^3e^{yx}+1/y

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(\partial)/(\partial x)(e^{xy}y^2+x/y)

\frac{\partial}{\partial x} (e^{x y} y^{2} + \frac{x}{y})

y^{3} e^{y x} + \frac{1}{y}

Solution steps

\frac{\partial}{\partial x} (e^{x y} y^{2} + \frac{x}{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (e^{x y} y^{2}) + \frac{\partial}{\partial x} (\frac{x}{y})

\frac{\partial}{\partial x} (e^{x y} y^{2}) = y^{3} e^{y x}

\frac{\partial}{\partial x} (\frac{x}{y}) = \frac{1}{y}

= y^{3} e^{y x} + \frac{1}{y}

\int e^{- \frac{x ^{2}}{2}} d x

\int_{0}^{1} \frac{x ^{4} + 3}{x} d x

y = \frac{1}{( 3 x + 8 ) ^{2}}

x \to - 3 lim (5 x)

- 2 9 s^{2} + 1

What is (\partial)/(\partial x)(e^{xy}y^2+x/y) ?
The answer to (\partial)/(\partial x)(e^{xy}y^2+x/y) is y^3e^{yx}+1/y